Problem: Simplify the following expression: $q = \dfrac{a^2 - 2a - 15}{a - 5} $
Explanation: First factor the polynomial in the numerator. $ a^2 - 2a - 15 = (a - 5)(a + 3) $ So we can rewrite the expression as: $q = \dfrac{(a - 5)(a + 3)}{a - 5} $ We can divide the numerator and denominator by $(a - 5)$ on condition that $a \neq 5$ Therefore $q = a + 3; a \neq 5$